Succinct Indices for Range Queries with applications to Orthogonal Range Maxima

We consider the problem of preprocessing $N$ points in 2D, each endowed with a priority, to answer the following queries: given a axis-parallel rectangle, determine the point with the largest priority in the rectangle. Using the ideas of the \emph{effective entropy} of range maxima queries and \emph{succinct indices} for range maxima queries, we obtain a structure that uses O(N) words and answers the above query in $O(\log N \log \log N)$ time. This is a direct improvement of Chazelle's result from FOCS 1985 for this problem -- Chazelle required $O(N/\epsilon)$ words to answer queries in $O((\log N)^{1+\epsilon})$ time for any constant $\epsilon > 0$.Comment: To appear in ICALP 201

Randomized controlled trial of an intervention to maintain suppression of HIV viremia after prison release: The impact trial

Background: HIV-infected individuals transitioning from incarceration to the community are at risk for loss of viral suppression. We compared the effects of imPACT, a multidimensional intervention to promote care engagement after release, to standard care on sustaining viral suppression after community re-entry. Methods: This trial randomized 405 HIV-infected inmates being released from prisons in Texas and North Carolina with HIV-1 RNA levels 0.99). Conclusions: Higher rates of HIV suppression and medical care engagement than expected based on previous literature were observed among HIV-infected patients with suppressed viremia released from prison. Randomization to a comprehensive intervention to motivate and facilitate HIV care access after prison release did not prevent loss of viral suppression. A better understanding of the factors influencing prison releasees' linkage to community care, medication adherence, and maintenance of viral suppression is needed to inform policy and other strategic approaches to HIV prevention and treatment

The asymptotic number of spanning trees in circulant graphs

Let T (G) be the number of spanning trees in graph G. In this note, we explore the asymptotics of T (G) when G is a circulant graph with given jumps. The circulant graph Cns1, s2, ..., sk is the 2 k-regular graph with n vertices labeled 0, 1, 2, ..., n - 1, where node i has the 2 k neighbors i ± s1, i ± s2, ..., i ± sk where all the operations are (mod n). We give a closed formula for the asymptotic limit limn → ∞ T (Cns1, s2, ..., sk)frac(1, n) as a function of s1, s2, ..., sk. We then extend this by permitting some of the jumps to be linear functions of n, i.e., letting si, di and ei be arbitrary integers, and examining under(lim, n → ∞) T (underover(C, n, s1, s2, ..., sk, ⌊ frac(n, d1) ⌋ + e1, ⌊ frac(n, d2) ⌋ + e2, ..., ⌊ frac(n, dl) ⌋ + el))frac(1, n) . While this limit does not usually exist, we show that there is some p such that for 0 ≤ q < p, there exists cq such that limit (1) restricted to only n congruent to q modulo p does exist and is equal to cq. We also give a closed formula for cq. One further consequence of our derivation is that if si go to infinity (in any arbitrary order), then under(lim, s1, s2, ..., sk → ∞) under(lim, n → ∞) T (underover(C, n, s1, s2, ..., sk))frac(1, n) = 4 exp [∫01 ∫01 ⋯ ∫01 ln (underover(∑, i = 1, k) sin2 π xi) d x1 d x2 ⋯ d xk] . Interestingly, this value is the same as the asymptotic number of spanning trees in the k-dimensional square lattice recently obtained by Garcia, Noy and Tejel. © 2009 Elsevier B.V. All rights reserved

Online maintenance of k-medians and k-covers on a line

The standard dynamic programming solution to finding k-medians on a line with n nodes requires O(kn2) time. Dynamic programming speed-up techniques, e.g., use of the quadrangle inequality or properties of totally monotone matrices, can reduce this to O(kn) time. However, these speed-up techniques are inherently static and cannot be used in an online setting, i.e., if we want to increase the size of the problem by one new point. Then, in the worst case, we could do no better than recalculating the solution to the entire problem from scratch in O(kn) time. The major result of this paper is to show that we can maintain the dynamic programming speed up in an online setting where points are added from left to right on a line. Computing the new k-medians after adding a new point takes only O(k) amortized time and O(k log n) worst-case time (simultaneously). Using similar techniques, we can also solve the online k-coverage with uniform coverage on a line problem with the same time bounds. © 2006 Springer Science+Business Media, Inc

The Knuth-Yao quadrangle-inequality speedup is a consequence of total-monotonicity

There exist several general techniques in the literature for speeding up naive implementations of dynamic programming. Two of the best known are the Knuth-Yao quadrangle inequality speedup and the SMAWK algorithm for finding the row-minima of totally monotone matrices. Although both of these techniques use a quadrangle inequality and seem similar they are actually quite different and have been used differently in the literature. In this paper we show that the Knuth-Yao technique is actually a direct consequence of total monotonicity. As well as providing new derivations of the Knuth-Yao result, this also permits showing how to solve the Knuth-Yao problem directly using the SMAWK algorithm. Another consequence of this approach is a method for solving online versions of problems with the Knuth-Yao property. The online algorithms given here are asymptotically as fast as the best previously known static ones. For example the Knuth-Yao technique speeds up the standard dynamic program for finding the optimal binary search tree of n elements from ⊖(n 3) down to O(n 2), and the results in this paper allow construction of an optimal binary search tree in an online fashion (adding a node to the left or right of the current nodes at each step) in O(n) time per step. We conclude by discussing how the general technique described here is also applicable to later extensions of the Knuth-Yao result, such as those devel oped by Borchers and Gupta

Unhooking circulant graphs: A combinatorial method for counting spanning trees and other parameters

Abstract. It has long been known that the number of spanning trees in circulant graphs with fixed jumps and n nodes satisfies a recurrence relation in n. The proof of this fact was algebraic (relating the products of eigenvalues of the graphs ’ adjacency matrices) and not combinatorial. In this paper we derive a straightforward combinatorial proof of this fact. Instead of trying to decompose a large circulant graph into smaller ones, our technique is to instead decompose a large circulant graph into different step graph cases and then construct a recurrence relation on the step graphs. We then generalize this technique to show that the number

PRIMARY HYPEROXALURIA TYPE-1 - GENOTYPIC AND PHENOTYPIC HETEROGENEITY

Primary hyperoxaluria type 1 (PH1) is an autosomal recessive disease caused by a deficiency of the liver-specific peroxisomal enzyme alanine: glyoxylate aminotransferase (AGT). The disease is notable for its extensive heterogeneity at the clinical, biochemical, enzymic and molecular genetic levels. A study of 116 PH1 patients over the past 8 years has revealed four main enzymic phenotypes: (1) absence of both AGT catalytic activity and immunoreactive AGT protein (similar to 40% of patients); (2) absence of AGT catalytic activity but presence of immunoreactive protein (similar to 16% of patients); (3) presence of both AGT catalytic activity and immunoreactive protein (similar to 41% of patients), in most of which cases the AGT is mistargeted to the mitochondria instead of the peroxisomes; and (4) a variation of the mistargeting phenotype in which AGT is equally distributed between peroxisomes and mitochondria, but in which that in the peroxisomes is aggregated into matrical core-like structures (similar to 3% of patients). Various point mutations, all occurring at conserved positions in the coding regions of the AGT gene, have been identified in these patients. The five mutations discussed in the present study, which have been found in individuals manifesting all of the four major enzymic phenotypes, account for the expressed alleles in about half of all Caucasian PH1 patients. The most common mutation found so far leads to a Gly170 --> Arg amino acid substitution. This mutation, in combination with a normally occurring Pro 11 --> Leu polymorphism, appears to be responsible for the unprecedented peroxisome-to-mitochondrion mistargeting phenotype

Pulmonary thromboembolism in AIDS patient with chronic venous insufficiency, pulmonary tuberculosis and breast cancer: a case report and pathophysiology review Tromboembolismo pulmonar em uma paciente com AIDS com insuficiência venosa profunda, tuberculose pulmonar e câncer de mama: relato de um caso e revisão da fisiopatologia

Recent literature reports thrombotic episodes occurring in patients with HIV infection associated with other abnormalities including neoplasms and infections predisposing to a hypercoagulable state. We report a 47-year-old woman who developed pulmonary thromboembolism in association with HIV infection, pulmonary tuberculosis and breast cancer. She was treated with rifampin, isoniazid, pyrazinamide; heparin, phenprocoumon, zidovudine, lamivudine and efavirenz. Acid fast bacilli were visualized in a sputum smear and three months after, Mycobacterium tuberculosis was isolated from lymph node biopsy during a episode of immune reconstitution. The isolated mycobacteria showed sensitivity to all first-line drugs. HIV infection, breast cancer and pulmonary tuberculosis have several mechanisms that induce hypercoagulable state and can lead to thromboembolic complications. Pulmonary thromboembolism in this patient was a diagnostic challenge because of all the other severe diseases that she experienced at the same time.<br>Publicações recentes relatam episódios trombóticos em pacientes infectados pelo HIV associados a outras condições que incluem neoplasias e infecções que predispõem para um estado de hipercoagulabilidade. Relata-se o caso de uma paciente de 47 anos portadora do HIV que desenvolveu tromboembolismo pulmonar, tuberculose pulmonar e câncer de mama. Foi tratada com rifampicina, isoniazida, pirazinamida, heparina, femprocumona, zidovudina, lamivudina e efavirenz. Bacilos ácido-álcool-resistentes foram observados no exame de escarro e três meses depois foi isolado o Mycobacterium tuberculosis da biópsia de linfonodo durante um episódio de reconstituição imune. A micobactéria isolada demonstrou sensibilidade a todas as drogas anti-tuberculosas de primeira linha. A infecção pelo HIV, o câncer de mama e a tuberculose pulmonar possuem vários mecanismos que induzem um estado de hipercoagulabilidade e que podem produzir complicações tromboembólicas incluindo o TEP nos pacientes com AIDS. O TEP nesta paciente foi um desafio diagnóstico, considerando todas as outras doenças graves que apresentou simultaneamente